Question

Шесть мальчиков и шесть девочек, среди которых Вася, Петя, Маша и Даша, участвуют в танцевальном номере. Сколькими способами их можно разбить на пары, если Вася не хочет танцевать с Машей, а Петя - с Дашей?

Answer 1

Получается 2 пари Вася-Даша
Петя-Маша

Answer 2

Calculation of Possible Pairings

To calculate the number of ways the six boys and six girls can be paired for the dance number, we need to consider the restrictions that Vasya does not want to dance with Masha and Petya does not want to dance with Dasha.

Let's break down the problem step by step:

1. We have six boys and six girls, which means we have 12 participants in total. 2. Since Vasya does not want to dance with Masha and Petya does not want to dance with Dasha, we need to exclude these pairings from the total number of possibilities. 3. We can calculate the number of ways to pair the remaining participants by using the concept of combinations.

To calculate the number of ways to pair the remaining participants, we can use the formula for combinations:

C(n, r) = n! / (r! * (n-r)!)

Where: - n is the total number of participants - r is the number of participants in each pairing

In this case, we have 10 remaining participants (excluding Vasya, Masha, Petya, and Dasha) and we need to pair them in groups of 2.

Using the combination formula, we can calculate the number of ways to pair the remaining participants:

C(10, 2) = 10! / (2! * (10-2)!)

Simplifying the equation:

C(10, 2) = 10! / (2! * 8!)

C(10, 2) = (10 * 9) / (2 * 1)

C(10, 2) = 45

Therefore, there are 45 possible ways to pair the six boys and six girls for the dance number, considering the restrictions mentioned.

Please note that the sources provided did not directly answer the question. The calculation was done using the concept of combinations.